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3 years ago

Which of the following properly describe "slope"? Select all that apply

Mathematics

1 answer:

son4ous [18]3 years ago

8 0

Boxes 1 and 4 apply :)

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Which statement is correct?

coldgirl [10]

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D. Secant is the reciprocal of cosine

Step-by-step explanation:

Secant is 1/cosine, so it is the reciprocal.

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3 years ago

And has enough seats for 312 people. How many seats are

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What is the first part of the question? Can you put it in the comments?

Step-by-step explanation:

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2 years ago

What does the letter p in the symbol 4p3 indicates?

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Probability is what the letter p indicates

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2 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$